Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(x³y²/z)⁰

Verified step by step guidance

1. Recall the property of exponents that any nonzero expression raised to the zero power equals 1, i.e., \(a^0 = 1\) for \(a \neq 0\).
2. Identify the base expression inside the parentheses: \(\left( \frac{x^3 y^5}{z} \right)\).
3. Apply the zero exponent to the entire base expression: \(\left( \frac{x^3 y^5}{z} \right)^0 = 1\).
4. Now consider the negative sign outside the parentheses: \(-\left( \frac{x^3 y^5}{z} \right)^0 = -1\).
5. Therefore, the simplified expression is \(-1\).

Key Concepts

Zero Exponent Rule

Any nonzero base raised to the zero power equals 1. For example, a^0 = 1 if a ≠ 0. This rule simplifies expressions where the exponent is zero, regardless of the complexity of the base.

Properties of Exponents

Exponent rules govern how to handle powers in multiplication, division, and powers of powers. Understanding these helps simplify expressions involving variables and exponents, such as (x^a y^b / z)^c.

Negative Sign Outside Parentheses

A negative sign placed before parentheses affects the entire expression inside. When simplifying, apply the negative sign after evaluating the expression inside the parentheses to ensure correct sign handling.